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UBC Theses and Dissertations

Entry flow problem of a liquid body into a suction pipette Yeung, Anthony Kwok-Cheung


The mathematical problem of the pipette aspiration of a liquid sphere is studied in the low Reynolds number limit. Two distinct models are proposed for the deforming body. They are: 1) a liquid droplet of constant viscosity, and 2) a viscoelastic cortex encapsulating an inviscid interior. These models represent energy dissipation distributed in the interior and on the surface of the body, respectively. Because the in-flow rates vary differently with the pipette size for the two models, this is suggested as a means of experimentally identifying the dominant region of viscous dissipation, and thus provide insight into the internal structure of the test sample. For the droplet problem, the linear Stokes equations are solved in the interior of the deforming body. The solutions, for some specified stress boundary conditions on a sphere, can be expressed as infinite sums of Legendre polynomials. In solving the surface flow problem, the complexities of the equations necessitate approximate solutions by computational means. A numerical procedure is developed which compares well with analytical results when the latter is available.

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